There are several differences between a crow and a blackbird. The two types of birds live in different ranges, are different sizes, have different beaks, tails and plumage and have different behaviors and vocalizations.
Two of the first things to consider are the location in which the bird is spotted and the bird's usual range. The common American crow is found throughout the continental US, while blackbirds are mostly found in the western and midwestern parts of the country.
Crows are also much bigger than blackbirds, but this may be difficult to tell without comparing the birds side-by-side. To estimate, consider the size of a pigeon. If the bird is larger than a pigeon, it is a probably a crow, and if it is smaller than a pigeon, it is most likely a blackbird.
There are also certain elements of a bird's plumage or the size of its beak and tail that can identify it. Blackbirds, for instance, may have yellow heads or red on their wings, while the common crow is entirely black.
There are also behavioral clues. Blackbirds and crows each have their own characteristic actions. For the crow these include flying in flocks, making a lot of noise and hopping while foraging for food.